Magnet

Chris has a \(2\times2\) square board. He wants to perform a Monte-Carlo simulation to find out the average distance between two points by randomly throwing two metal beads on the board and measure their distance. However, his brother Patrick secretly hid a magnet below one of the quadrants such that 70% of the metal beads will land uniformly on that area, and 30% of the metal beds will land uniformly in the other quadrants.

Chris is very confused as the answer doesn't match the one in his computation. Instead, what is the answer Chris found?

Give your answer to 4 decimal places.

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